Okay well this week was one of the easier weeks for me because I had more time to review domain and range. I understand the functions and reflections because all you have to do is know the equations from the notes and plug in for what the problem is asking. If you are having trouble with this, let me know.
example: (f+g)(x)= add f(x) & g(x)
this equation is also used when subtracting, multiplying, and dividing.
If you see (FoG)(x)=f(g(x))=composite.
**Reflecting
To reflect on the x axis, put a - in front of the equation
example: y=x^2
1. x axis--- y= -x^2 No
To reflect on the y axis, plug in (- )
2. y axis---y= (-x)^2
= x^2 Yes
To reflect on y=x find the inverse
a. switch x & y
b. solve for y
3. y= x
x=y^2
y= square root of x No
To reflect on the origin, find x & y axis.
4. origin
y=-(-x^2)
y=-x^2 No
I am having trouble with 4.5. -finding inverses and proving them. If anyone can help with inverses it would help alot!!!
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Finding an inverse should be a quick problem on a test. Solving is very straight forward and simple if you discover a way to simplify the steps and memorize your simplification.
ReplyDeleteSimple steps for inverse finding
• Use horizontal line test (this is where you sketch the equation on a graph then draw a horizontal line anywhere and check to see whether it hits the sketched object once or twice) * remember if it touches twice then there is no inverse
• (if the equation passes the horizontal line test) Switch the X and Y
• Solve for Y
EX: y=5x-2
• Sketch a graph for the horizontal line test. * it passes
• Switch the X and Y * x=5y-2
• Solve for Y * x-2=5y therefore y= x+2/5
Next you’ll have to prove
Steps for proving an inverse
• Plug the inverse in *you’ll plug it into the first formula
* this formula is f(f-1(x)) = X
• Plug the inverse in * you’ll plug it into the second formula
* this formula is f-1(f(x)) = X
Ex: *y=5(x+2/5)-2 = x+2-2 = x
*y=(5x-2)/5+2 = x-2+2 = x
If each of the answers to the formulas are both = X then you completed the problem correctly